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according added addition alternative Apollonius appears Aristotle assumed axiom base Book called centre circle coincide commentary Common Notion conclusion congruent construction contained converse definition described direction distance draw drawn edition Elements enunciation equal Euclid existence explain expression extremity fact figure follows geometry given gives greater Greek hand Heiberg Hence Heron hypothesis impossible included joined latter lemma length less magnitude means meet mentioned method namely necessary objection observed opposite original Pappus parallel parallelogram particular passage perpendicular plane position possible postulate principles problem Proclus produced proof proposition proved quoted reason rectangle reference regards remaining remarks respectively right angles says scholia seems segment sense sides similar solid square straight line suppose surface taken takes term theorem things translation triangle triangle ABC true whole
Page 322 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 259 - If two triangles have two sides of the one equal to two sides of the...
Page 188 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 204 - In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Page 162 - A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Page 167 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Page 257 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 176 - Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.